(1) Dipartimento di Matematica e Informatica, Università di Perugia, Via Vanvitelli 1, 06123 Perugia, Italy
Abstract:
We explicitly solve the existence problem for 1-rotational k-cycle systems of the complete graph Kv with v1 or k (mod 2k). For v1 (mod 2k) we have existence if and only if k is an odd composite number. For any odd k and vk (mod 2k), (except k3 and v15, 21 (mod 24)) a 1-rotational k-cycle system of Kv exists.Final version received: June 18, 2003